# Ex.13.1 Q1 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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## Question

Following are the car parking charges near a railway station up to

$$4$$ hours           ₹$$60$$

$$8$$ hours           ₹$$100$$

$$12$$ hours        ₹$$140$$

$$24$$ hours        ₹$$180$$

Check if the parking charges are in direct proportion to the parking time.

## Text Solution

What is Known?

Parking charges for different hours.

What is Unknown?

Parking charges are direct proportion to the parking time or not.

Reasoning:

If two quantities are related in such a way that an increase in one lead to a corresponding proportional increase in the other, then such a variation is called direct variation.

Steps:

The parking charge for $$1$$ hour in all the four cases then the variation is direct.

We have:

\begin{align}\frac{{60}}{4}&=\frac{{15}}{1}\\&=15\\\frac{{100}}{8}&=\frac{{25}}{2}\\ &= 12.5\\\frac{{140}}{{12}} &=\frac{{35}}{3}\\&=11.67\\\frac{{180}}{{24}}&=\frac{{15}}{2}\\&= 7.50\end{align}

Since all the values are not the same, the parking charges are not in direct proportion to parking times.

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